In exponential-time algorithmics [1]}, the aim is to design algorithms for NP-hard problems with the natural objective to minimize their running times.
In this paper, we consider a broad class of subset problems, where for an input instance \(I\)  on a universe \(U_I\) , the question is whether there is a subset \(S\)  of the universe satisfying certain properties.
For example, in the Feedback Vertex Set problem, the input instance consists of a graph \(G=(V,E)\)  and an integer \(k\) , the universe is the vertex set and the property to be satisfied by a subset \(S\)  is the conjunction of “\(|S|\le k\) ” and “\(G-S\)  is acyclic”.
